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"through solving" is correct and usable in written English.
You can use it when you want to emphasize how someone has come to a solution. For example, "He was able to fix the problem through solving a difficult equation."
Exact(60)
The design method is fulfilled through solving linear matrix inequalities.
My father's expression of love was entirely through solving problems for us.
Methods of computing will be taught through solving a variety of physical science problems.
The stress field can be obtained through solving a mixed variational problem.
The design aspects of the device are explored through solving several examples.
Furthermore, the suitable solvers are also analyzed through solving each subproblem.
The induced ∞-norm FIR filter is designed through solving linear matrix inequalities (LMIs) iteratively.
The identified parameters are obtained through solving the estimation equations by simple least square method.
Frequencies and vibration mode shapes are determined through solving an eigenvalue problem.
Hence the vibration solutions can be obtained through solving the eigenvalue problem.
They then had to work out URLs and IP addresses through solving a series of clues until they reached the final stage.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com